1. Field of the Invention
The invention relates to a machining apparatus including a control device for controlling a tool by means of which a part is to be machined on the basis of a predetermined geometry, which control device combines a spline interpolation device with path-determining means for determining a path of the tool on the basis of parametrized splines. The invention further relates to a control device suitable for use in such a machining apparatus.
2. Description of the Related Art
Such a machining apparatus is known from the article "Durchgangiges Spline-Konzept", V. Reetz, Energie und Automation 11 (1989), Special "EMO" 1989, pp. 19-20. This article discloses how for machining complicated parts use is made of spline interpolation in order to be able to describe, in contrast with linear and circular interpolation methods, a part geometry with a minimum number of supporting points. Splines, i.e. polynomials of higher degree, of the third order are used to describe path segments, it being ensured that successive path segments adjoin each other as closely as possible, that is to say that it is ensured that the contour or path to be machined is as smooth as possible. Further, the splines, which are parametrized in terms of arc length, are parametrized so that the spatial speed of the tool to be controlled is substantially constant along the contour to be machined. A spline is then characterized by multi-axis end point coordinates of a path segment, the value of the path parameter at the beginning point of a polynomial (the path length) and the coefficients of the third degree axis polynomials. The calculation of a spline polynomial can be started from a part contour determined by means of a CAD program or from a contour obtained by digitization or scanning. Adaptation of the spline to a contour is effected on the basis of approximation methods, such as a Newton approximation method.
With splines determined in the manner described above, a substantially linear relation will exist between the path covered by the tool and the parameter value, which relation is expressed in terms of arc length. However, in the case of arbitrary splines, such as splines directly originating from a CAD program, such a linear relation will generally not exist. That is to say, the arc length variation, which increases monotonically with an increase of the parameter value, will not increase linearly (at a constant rate) when the parameter value increases linearly. As a result, although the average speed of the tool over a path segment is constant, it is true, the instantaneous speed along the spline varies.